Write an equation of the line that is parallel to 3x + 9y = 7 and passes through the point (6, 4). a) y = 3x - 26 b) y = -3x + 16 c) y = 1/3 x-2 d) y = -1/3 x+6

D)y = -1/3 x+6

Step-by-step explanation:

If we want to find a line parallel to 3x+9y=7, the slopes will have to be the same because parallel lines have the same slope.  Knowing y= mx+b we need to find the slope of the old line.

3x+9y=7

Subtract 3x from each side

3x-3x +9y = -3x+7

9y = -3x+7

Divide each side by 9

9y/9 = -3x/9 + 7/9

y = -1/3 x + 7/9

We know the slope of the  old line is -1/3, so the slope of the parallel line is -1/3.

If we know the slope of the line and a point, we can use the point slope form of a line

y-y1 = m(x-x1)

y-4 = -1/3(x-6)

Distribute the -1/3

y-4 = -1/3 x -1/3*-6

y-4 = -1/3x +2

Add 4 to each side

y-4+4 = -1/3x +2+4

y = -1/3x+6

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.

the slope of the line is 60

one point on the line is (40,10)

step-by-step explanation:

in the equation outside the parenthesis the equation always tells you the slope. in this case it is 60.

in the parenthesis is also says 40 which is x because it is near the x and 10 is y because it is near y.